Normal: Equations

As mentioned earlier, this won’t be much complicated and all equations will be based on one simple fact – ‘the normal to a circle always passes through its center’. Let’s begin.

Equation of a normal to the circle x2 + y2 = a2 at a given point (x1, y1)

Here’s what the situation looks like:

The given normal passes through the point (x1, y1­) and will also pass through the center of the circle, i.e (0, 0). Now, to find the equation of the normal, all we have to do is use the two-point form of the equation of a straight line.

Lastly, similar to case (3), using the point-slope form, the equation of the normal will be (y + f) = m(x + g)

That pretty much covers everything about equations to the normals. The next lesson will cover a few examples, and also one very important application of normals – finding the shortest distance between two curves.